Quasiparticle branch mixing rates in superconducting aluminum

The kinetic equation is used to compute the elastic and inelastic quasiparticle branch mixing rates for a superconducting film into which quasiparticles are injected via a tunnel barrier from a second superconducting film. Representative graphs are presented of the steady-state quasiparticle distribution, the quasiparticle charge imbalance Q* versus injection current, the charge relaxation rate τQ*-1 vs Δ/kBTc for several values of elastic scattering rate, and the quasiparticle branch relaxation rate τQ-1 as a function of energy. The quasiparticle potential developed in the injection film is related to τQ-1 and thence to τ0-1 a characteristic electron-phonon scattering time. Detailed measurements of τQ are reported for films of superconducting A1, some of which were doped with oxygen to give a range of transition temperatures from 1.2 to 2.1 K. From the dependence of τQ*-1 on Δ/kBTc, values are deduced for the gap anisotropy of the films. In the cleanest samples, τ0=0.10±0.02 μ sec, a value that is in good agreement with energy-gap relaxation and 2Δ- phonon (phonons of energy ≳2Δ) mean-free-path measurements, but a factor of about 4 smaller than that obtained from recombination time measurements and theoretical calculations. The value of τ0-1 in the A1 films increases with the transition temperature Tc as Tc5 or Tc6, instead of Tc3 as predicted by simple theory. It is suggested that the rapid increase of τ0-1 with Tc may arise from either a strong dependence of α2F(ω) on Tc or from a small concentration of magnetic impurities.